TSTP Solution File: HEN007-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : HEN007-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 13:00:51 EDT 2022
% Result : Unsatisfiable 0.99s 1.29s
% Output : Refutation 0.99s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : HEN007-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n026.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Fri Jul 1 14:00:19 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.99/1.29 ============================== Prover9 ===============================
% 0.99/1.29 Prover9 (32) version 2009-11A, November 2009.
% 0.99/1.29 Process 26934 was started by sandbox2 on n026.cluster.edu,
% 0.99/1.29 Fri Jul 1 14:00:20 2022
% 0.99/1.29 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_26672_n026.cluster.edu".
% 0.99/1.29 ============================== end of head ===========================
% 0.99/1.29
% 0.99/1.29 ============================== INPUT =================================
% 0.99/1.29
% 0.99/1.29 % Reading from file /tmp/Prover9_26672_n026.cluster.edu
% 0.99/1.29
% 0.99/1.29 set(prolog_style_variables).
% 0.99/1.29 set(auto2).
% 0.99/1.29 % set(auto2) -> set(auto).
% 0.99/1.29 % set(auto) -> set(auto_inference).
% 0.99/1.29 % set(auto) -> set(auto_setup).
% 0.99/1.29 % set(auto_setup) -> set(predicate_elim).
% 0.99/1.29 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.99/1.29 % set(auto) -> set(auto_limits).
% 0.99/1.29 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.99/1.29 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.99/1.29 % set(auto) -> set(auto_denials).
% 0.99/1.29 % set(auto) -> set(auto_process).
% 0.99/1.29 % set(auto2) -> assign(new_constants, 1).
% 0.99/1.29 % set(auto2) -> assign(fold_denial_max, 3).
% 0.99/1.29 % set(auto2) -> assign(max_weight, "200.000").
% 0.99/1.29 % set(auto2) -> assign(max_hours, 1).
% 0.99/1.29 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.99/1.29 % set(auto2) -> assign(max_seconds, 0).
% 0.99/1.29 % set(auto2) -> assign(max_minutes, 5).
% 0.99/1.29 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.99/1.29 % set(auto2) -> set(sort_initial_sos).
% 0.99/1.29 % set(auto2) -> assign(sos_limit, -1).
% 0.99/1.29 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.99/1.29 % set(auto2) -> assign(max_megs, 400).
% 0.99/1.29 % set(auto2) -> assign(stats, some).
% 0.99/1.29 % set(auto2) -> clear(echo_input).
% 0.99/1.29 % set(auto2) -> set(quiet).
% 0.99/1.29 % set(auto2) -> clear(print_initial_clauses).
% 0.99/1.29 % set(auto2) -> clear(print_given).
% 0.99/1.29 assign(lrs_ticks,-1).
% 0.99/1.29 assign(sos_limit,10000).
% 0.99/1.29 assign(order,kbo).
% 0.99/1.29 set(lex_order_vars).
% 0.99/1.29 clear(print_given).
% 0.99/1.29
% 0.99/1.29 % formulas(sos). % not echoed (13 formulas)
% 0.99/1.29
% 0.99/1.29 ============================== end of input ==========================
% 0.99/1.29
% 0.99/1.29 % From the command line: assign(max_seconds, 300).
% 0.99/1.29
% 0.99/1.29 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.99/1.29
% 0.99/1.29 % Formulas that are not ordinary clauses:
% 0.99/1.29
% 0.99/1.29 ============================== end of process non-clausal formulas ===
% 0.99/1.29
% 0.99/1.29 ============================== PROCESS INITIAL CLAUSES ===============
% 0.99/1.29
% 0.99/1.29 ============================== PREDICATE ELIMINATION =================
% 0.99/1.29
% 0.99/1.29 ============================== end predicate elimination =============
% 0.99/1.29
% 0.99/1.29 Auto_denials:
% 0.99/1.29 % copying label prove_zQyLEzQx to answer in negative clause
% 0.99/1.29
% 0.99/1.29 Term ordering decisions:
% 0.99/1.29 Function symbol KB weights: zero=1. x=1. y=1. z=1. identity=1. zQx=1. zQy=1. divide=1.
% 0.99/1.29
% 0.99/1.29 ============================== end of process initial clauses ========
% 0.99/1.29
% 0.99/1.29 ============================== CLAUSES FOR SEARCH ====================
% 0.99/1.29
% 0.99/1.29 ============================== end of clauses for search =============
% 0.99/1.29
% 0.99/1.29 ============================== SEARCH ================================
% 0.99/1.29
% 0.99/1.29 % Starting search at 0.01 seconds.
% 0.99/1.29
% 0.99/1.29 ============================== PROOF =================================
% 0.99/1.29 % SZS status Unsatisfiable
% 0.99/1.29 % SZS output start Refutation
% 0.99/1.29
% 0.99/1.29 % Proof 1 at 0.26 (+ 0.02) seconds: prove_zQyLEzQx.
% 0.99/1.29 % Length of proof is 39.
% 0.99/1.29 % Level of proof is 19.
% 0.99/1.29 % Maximum clause weight is 23.000.
% 0.99/1.29 % Given clauses 176.
% 0.99/1.29
% 0.99/1.29 1 less_equal(zero,A) # label(zero_is_smallest) # label(axiom). [assumption].
% 0.99/1.29 3 less_equal(x,y) # label(xLEy) # label(hypothesis). [assumption].
% 0.99/1.29 4 quotient(z,y,zQy) # label(zQy) # label(hypothesis). [assumption].
% 0.99/1.29 5 quotient(z,x,zQx) # label(zQx) # label(hypothesis). [assumption].
% 0.99/1.29 6 quotient(A,B,divide(A,B)) # label(closure) # label(axiom). [assumption].
% 0.99/1.29 7 -less_equal(zQy,zQx) # label(prove_zQyLEzQx) # label(negated_conjecture) # answer(prove_zQyLEzQx). [assumption].
% 0.99/1.29 8 -less_equal(A,B) | quotient(A,B,zero) # label(quotient_less_equal) # label(axiom). [assumption].
% 0.99/1.29 9 -quotient(A,B,zero) | less_equal(A,B) # label(less_equal_quotient) # label(axiom). [assumption].
% 0.99/1.29 10 -quotient(A,B,C) | less_equal(C,A) # label(divisor_existence) # label(axiom). [assumption].
% 0.99/1.29 11 -less_equal(A,B) | -less_equal(B,A) | A = B # label(less_equal_and_equal) # label(axiom). [assumption].
% 0.99/1.29 12 -quotient(A,B,C) | -quotient(A,B,D) | C = D # label(well_defined) # label(axiom). [assumption].
% 0.99/1.29 13 -quotient(A,B,C) | -quotient(B,D,E) | -quotient(A,D,F) | -quotient(F,E,V6) | -quotient(C,D,V7) | less_equal(V6,V7) # label(quotient_property) # label(axiom). [assumption].
% 0.99/1.29 14 quotient(x,y,zero). [hyper(8,a,3,a)].
% 0.99/1.29 16 quotient(zero,A,zero). [hyper(8,a,1,a)].
% 0.99/1.29 17 -quotient(zQy,zQx,zero) # answer(prove_zQyLEzQx). [ur(9,b,7,a)].
% 0.99/1.29 18 less_equal(divide(A,B),A). [hyper(10,a,6,a)].
% 0.99/1.29 22 divide(z,x) = zQx. [hyper(12,a,6,a,b,5,a)].
% 0.99/1.29 42 less_equal(divide(zQy,zero),divide(zQx,y)). [hyper(13,a,6,a,b,14,a,c,4,a,d,6,a,e,6,a),rewrite([22(6)])].
% 0.99/1.29 91 quotient(divide(A,B),A,zero). [hyper(8,a,18,a)].
% 0.99/1.29 106 less_equal(divide(divide(A,A),zero),zero). [hyper(13,a,6,a,b,91,a,c,6,a,d,6,a,e,91,a)].
% 0.99/1.29 121 quotient(divide(zQy,zero),divide(zQx,y),zero). [hyper(8,a,42,a)].
% 0.99/1.29 127 divide(divide(A,A),zero) = zero. [hyper(11,a,1,a,b,106,a),flip(a)].
% 0.99/1.29 160 quotient(divide(A,A),zero,zero). [para(127(a,1),6(a,3))].
% 0.99/1.29 166 less_equal(divide(A,A),zero). [hyper(9,a,160,a)].
% 0.99/1.29 167 divide(A,A) = zero. [hyper(11,a,1,a,b,166,a),flip(a)].
% 0.99/1.29 170 quotient(A,A,zero). [para(167(a,1),6(a,3))].
% 0.99/1.29 174 less_equal(divide(divide(A,divide(A,zero)),zero),zero). [hyper(13,a,6,a,b,16,a,c,6,a,d,6,a,e,170,a)].
% 0.99/1.29 184 less_equal(divide(divide(divide(zQy,zero),zQx),zero),zero). [hyper(13,a,121,a,b,91,a,c,6,a,d,6,a,e,16,a)].
% 0.99/1.29 221 divide(divide(A,divide(A,zero)),zero) = zero. [hyper(11,a,1,a,b,174,a),flip(a)].
% 0.99/1.29 224 divide(divide(divide(zQy,zero),zQx),zero) = zero. [hyper(11,a,1,a,b,184,a),flip(a)].
% 0.99/1.29 437 quotient(divide(A,divide(A,zero)),zero,zero). [para(221(a,1),6(a,3))].
% 0.99/1.29 449 less_equal(divide(A,divide(A,zero)),zero). [hyper(9,a,437,a)].
% 0.99/1.29 451 divide(A,divide(A,zero)) = zero. [hyper(11,a,1,a,b,449,a),flip(a)].
% 0.99/1.29 452 quotient(A,divide(A,zero),zero). [para(451(a,1),6(a,3))].
% 0.99/1.29 504 less_equal(A,divide(A,zero)). [hyper(9,a,452,a)].
% 0.99/1.29 506 divide(A,zero) = A. [hyper(11,a,18,a,b,504,a)].
% 0.99/1.29 590 divide(zQy,zQx) = zero. [back_rewrite(224),rewrite([506(3),506(5)])].
% 0.99/1.29 642 quotient(zQy,zQx,zero). [para(590(a,1),6(a,3))].
% 0.99/1.29 643 $F # answer(prove_zQyLEzQx). [resolve(642,a,17,a)].
% 0.99/1.29
% 0.99/1.29 % SZS output end Refutation
% 0.99/1.29 ============================== end of proof ==========================
% 0.99/1.29
% 0.99/1.29 ============================== STATISTICS ============================
% 0.99/1.29
% 0.99/1.29 Given=176. Generated=15223. Kept=642. proofs=1.
% 0.99/1.29 Usable=100. Sos=169. Demods=41. Limbo=0, Disabled=385. Hints=0.
% 0.99/1.29 Megabytes=0.42.
% 0.99/1.29 User_CPU=0.26, System_CPU=0.02, Wall_clock=0.
% 0.99/1.29
% 0.99/1.29 ============================== end of statistics =====================
% 0.99/1.29
% 0.99/1.29 ============================== end of search =========================
% 0.99/1.29
% 0.99/1.29 THEOREM PROVED
% 0.99/1.29 % SZS status Unsatisfiable
% 0.99/1.29
% 0.99/1.29 Exiting with 1 proof.
% 0.99/1.29
% 0.99/1.29 Process 26934 exit (max_proofs) Fri Jul 1 14:00:20 2022
% 0.99/1.29 Prover9 interrupted
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